Find The surface area of the pyramid

Answer:

n = 2

Step-by-step explanation:

[tex]\sqrt{2n+28}-4\sqrt{n}=0\\\\\\\sqrt{2n+28} = 4\sqrt{n}\\\\[/tex]

Take square,

[tex](\sqrt{2n+28})^{2}=( 4\sqrt{n})^{2}\\\\ 2n + 28 = 16n\\\\28 = 16n -2n\\\\28 =14n\\\\14n=28\\\\n=\frac{28}{14}\\\\n=2[/tex]

Answer:

n=2

Step-by-step explanation:

got it right on edge

Answer:

Stratified sampling

Step-by-step explanation:

The is a type of sampling in which the population of interest is divided into subpopulations and then each subpopulation is randomly sampled.

In this case study, instead of just doing a random sampling of all students, the research divided the population of all students into subpopulations which includes freshmen, sophomores, juniors and seniors and then she makes a random sampling of each of these subpopulations.

Answer:

x = 95°

Step-by-step explanation:

[tex]x = ?\\Sum -of- interior -angles=?\\Shape = pentagon\\No -of - sides= 5\\Sum- of- interior- angles = (n-2)180\°\\=(5-2)\times180\°\\3\times180\°\\Sum-of-interior-angles=540\°\\104\°+117\°+100\°+124\°+x\°=540\°\\445\°+x\° = 540\°\\x\° = 540\°-445\°\\x = 95\°[/tex]

Answer:

The times are t = 9, t = 10, t = 11 and t = 12

Step-by-step explanation:

For the train to be more than 16 km South and since south is taken as negative,

d(t) > -16

t³ - 9t² + 6t > -16

t³ - 9t² + 6t + 16 > 0

Since -1 is a factor of 16, inserting t = -1 into the d(t), we have

d(-1) = (-1)³ - 9(-1)² + 6(-1)+ 16 = -1 - 9 - 6 + 16 = -16 + 16 = 0. By the factor theorem, t + 1 is a factor of d(t)

So, d(t)/(t + 1) = (t³ - 9t² + 6t + 16)/(t +1) = t² - 10t + 16

Factorizing  t² - 10t + 16, we have

t² - 2t - 8t + 16

= t(t - 2) - 8(t - 2)

= (t -2)(t - 8)

So t - 2 and t - 8 are factors of d(t)

So (t + 1)(t -2)(t - 8) > 0

when t < -1, example t = -2 ,(t + 1)(t -2)(t - 8) = (-2 + 1)(-2 -2)(-2 - 8) = (-1)(-4)(-10) = -40 < 0

when -1 < t < 2, example t = 0 ,(t + 1)(t -2)(t - 8) = (0 + 1)(0 -2)(0 - 8) = (1)(-2)(-8) = 16 > 0

when 2 < t < 8, example t = 3 ,(t + 1)(t -2)(t - 8) = (3 + 1)(3 -2)(3 - 8) = (4)(1)(-5) = -20 < 0

when t > 8, example t = 9,(t + 1)(t -2)(t - 8) = (9 + 1)(9 -2)(9 - 8) = (10)(7)(1) = 70 > 0

Since t cannot be negative, d(t) is positive in the interval 0 < t < 2 and t > 8

Since t ∈ (0, 12]

In the interval 0 < t < 2 the only value possible for t is t = 1

d(1) = t³ - 9t² + 6t = (1)³ - 9(1)² + 6(1) = 1 - 9 + 6 = -2

Since d(1) < -16 this is invalid

In the interval t > 8 , the only possible values of t are t = 9, t = 10.t = 11 and t = 12.

So,

d(9) = 9³ - 9(9)² + 6(9) = 0 + 54 = 54 km

d(10) = 10³ - 9(10)² + 6(10) = 1000 - 900 + 60 = 100 +60 = 160 km

d(11) = 11³ - 9(11)² + 6(11) = 1331 - 1089 + 66 = 242 + 66 = 308 km

d(12) = 12³ - 9(12)² + 6(12) = 1728 - 1296 + 72 = 432 + 72 = 504 km

Answer:

a = 1

Step-by-step explanation:

The factor in front of x must be the same in both equations.

So (a+2) in the first must be 3 (like it is in the second).

That is the case when a=1.

So the +7 and the -4 are not relevant!

Answer: Population density the United Kingdom [tex]=2.63\times10^2[/tex]

A= 2.63

B= 2

Step-by-step explanation:

We know that, to calculate the population density, we will divide the population by the size of the area.

i.e. [tex]\text{Population density}=\dfrac{\text{Population size}}{\text{Area}}[/tex]

Given : Area of UK = 243,610 km²1

Population = [tex]6.41 \times 10^7[/tex]

Then, the population density the United Kingdom would be :

[tex]\text{Population density}=\dfrac{6.41 \times 10^7}{243,610}\\\\=\dfrac{64100000}{243610}=263.125487459\\\\\approx263=2.63\times10^2[/tex]

On comparing to [tex]A\times10^B[/tex], we get

A= 2.63

B= 2

━━━━━━━☆☆━━━━━━━

▹ Answer

72 Chocolate Chips

▹ Step-by-Step Explanation

1 Pancake = 8 Chocolate Chips

You can set this up as:

[tex]\frac{1}{8} = \frac{9}{y} \\\\1 * 9 = 9\\8 * 9 = 72\\\\y = 72\\[/tex]

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer: 12 friends.

Step-by-step explanation:

the data we have is:

Mei Su had 80 coins.

She gave the coins to her friends, in such a way that every friend got a different number of coins, then we have that:

The maximum number of friends that could have coins is when:

friend 1 got 1 coin

friend 2 got 2 coins

friend 3 got 3 coins

friend N got N coins

in such a way that:

(1 + 2 + 3 + ... + N) ≥ 79

I use 79 because "she gave most of the coins", not all.

We want to find the maximum possible N.

Then let's calculate:

1 + 2 + 3 + 4 + 5 = 15

15 + 6 + 7 + 8 + 9 + 10 = 55

now we are close, lets add by one number:

55 + 11 = 66

66 + 12 = 78

now, we can not add more because we will have a number larger than 80.

Then we have N = 12

This means that the maximum number of friends is 12.

Answer:

12

Step-by-step explanation:

my

Answer:

option B is the correct option.

Solution,

[tex] {(x - 4)}^{2} = 5 \\ [/tex]

x-4=_+√5

X=4_+√5

Hope this helps...

Good luck on your assignment...

Answer:

(x-4)^2 =5

x^2-16=5

x^2=5+16

x^2=21

√x^2=√21

x=√21

Step-by-step explanation :

First of all open the bracket which has square

Secondly change the position of 16

Note: when a number changes its place , the symbol also changes

then when you get the value take the square root on both sides

and you'll get the answer

Answer:

53

Step-by-step explanation:

Explicit Formula: an = a1 + d(n - 1)

Simply plug in your known variables:

an = 8 + 3(n - 1)

Then plug in 16 for n:

a(16) = 8 + 3(16 - 1)

a(16) = 8 + 3(15)

a(16) = 8 + 45

a(16) = 53

Answer:

53

Step-by-step explanation:

an = dn + (a - d)

an = 3n + 8  - 3

an = 3n + 5

Put n as 16 and solve.

3(16) + 5

48 + 5

= 53

Answer:

6080 cm OR 60.8m

Step-by-step explanation:

75 x 40 = 3000 cm

77 x 40 = 3080 cm

They are moving in perfectly opposite directions, which makes a straight line.

3000 + 3080 = 6080 cm = 60.8m

Answer:

B is P(x)=(x-3)^2 +2

C is P(x)=(x-1)^2 -5

Step-by-step explanation:

i think i am right

Answer:

DC = 1.92 inches

AD = 11.08 inches

Step-by-step explanation:

From the figure given above, angle ABC is a right angle triangle where

AB = 12 inches

BC = 5 inches

Use pythagorean theorem to find AC

AC^2 = AB^2 + BC^2

Substitutes all the parameters into the formula

AC^2 = 12^2 + 5^2

AC^2 = 144 + 25

AC = sqrt ( 169 )

AC = 13 in

Also,

BD^2 = AB^2 - AD^2

Let AD = 13 - x

Substitute all into the formula

BD^ = 12^2 - (13 - x)^2 ..... (1)

Moreso,

BD^2 = BC^2 - DC^2

Let DC = x

Substitute all into the formula

BD^2 = 5^2 - x^2 ...... (2)

Equate equation 1 and 2

12^2 - ( 13 - x )^2 = 5^2 - x^2

144 - (169 - 26x + x^2) = 25 - x^2

Open the bracket

144 - 169 + 26x - x^2 = 25 - x^2

-25 + 26x = 25

Collect the like terms

26x = 50

X = 50/26

X = 1.92 inches

Therefore, DC = 1.92 inches

And AD = 13 - 1.92 = 11.08 inches

Step-by-step explanation:

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the car travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars?

Solution :

Let “x km/hr” be the speed of 1st car

Let “y km/hr” be the speed of the 2nd car

Time = Distance/Speed

Speed of both cars while they are traveling in the same direction = (x – y)

Speed of both cars while they are traveling in the opposite direction = (x + y)

5 = 100/(x -y)

x – y = 100/5

x - y = 20

x - y - 20 = 0 ---(1)

1 = 100/(x + y)

x + y = 100

x + y - 100 = 0--b----(2)

x/(100 + 20) = y/(-20 + 100) = 1/(1 + 1)

x/120 = y/80 = 1/2

x/120 = 1/2 y/80 = 1/2

x = 120/2 y = 80/2

x = 60 y = 40

So, the speed of first car = 60 km/hr

Speed of second car = 40 km/hr

Answer:

The population of the city was 25,000 in 1970 and 1983.

Step-by-step explanation:

In order to find the year at which the population was 25,000 we need to make p(t) equal to that number and solve for t as shown below.

[tex]25000 = 14*t^2 + 650*t + 32000\\14*t^2 + 650*t + 7000 = 0\\t^2 + 46.43*t + 500 = 0\\t_{1,2} = \frac{-46.43 \pm \sqrt{(46.43)^2 - 4*1*500}}{2}\\t_{1,2} = \frac{-46.43 \pm \sqrt{155.75}}{2}\\t_{1,2} = \frac{-46.43 \pm 12.48}{2}\\t_1 = \frac{-33.95}{2} = -16.98\\t_2 = \frac{-58.91}{2} =- 29.5[/tex]

Since t = 0 corresponds to the year 2000, then t1 = 1983 and t2 = 1970.

Answer:

6.552×10³×10

6.552×10^3+1

6.552×10^4 is the standard form

i hope this will help you :)

Answer:

5x4^10

Step-by-step explanation:

Hope this helps have a nice day :)

Answer:

5. [tex]4^{9}[/tex]

Step-by-step explanation:

There is a common ratio r between consecutive terms, that is

r = 20 ÷ 5 = 80 ÷ 20 = 320 ÷ 80 = 4

This indicates the sequence is geometric with n th term

[tex]a_{n}[/tex] = a . [tex]r^{n-1}[/tex]

Here a = 5 and r = 4 , thus

[tex]a_{10}[/tex] = 5. [tex]4^{9}[/tex]

Answer:

∠APD and ∠CPB are Vertical Angles

Equation: 6x - 10 = 4x + 8

Step-by-step explanation:

We use the Vertical Angles Theorem to solve for x:

Step 1: Set up equation

6x - 10 = 4x + 8

Step 2: Subtract 4x on both sides

2x - 10 = 8

Step 3: Add 10 to both sides

2x = 18

Step 4: Find x by dividing 2 on both sides

x = 9

Step 5: Plug in x for 9 to find degree measure

m∠CPB = 4(9) + 8

m∠CPB = 36 + 8

m∠CPB = 44°

m∠CPB = m∠APD (Vertical Angles)

m∠APD = 44°

Answer:

[tex]\boxed{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

∠APD and ∠CPB are vertically opposite angles

The equation is 6x-10=4x+8

[tex]6x-10=4x+8\\6x-4x=8+10\\2x=18\\x=9[/tex]

Plug x as 9 for the angle.

[tex]4(9)+8\\36+8\\44[/tex]

∠APD and ∠CPB = 44 degrees

Answer:

Out of 8000 students, 10% take tuition in various subjects before the exam.

10% of 8000 is:

10/100 * 8000 = 800

Among the 800, 40% take tuition in English only and 20% take tuition in Math only.

80 students take tuition in other subjects, therefore, in percentage:

80/800 * 100 = 10%

Therefore, the percentage of students that take tuition in both Math and English is:

100% - (40% + 20% + 10%) = 100% - 70% = 30%

30% of the 800 students take tuition in both subjects. That is:

30/100 * 800 = 240 students

Therefore, among the 8000 students in the district, only 240 take tuition in both English and Math.

In percentage:

240/8000 * 100 = 3%

3% of students take tuition in both English and Math.

In Ratio:

3 : 100

3 out of 100 students take tuition in English and Math.

Answer:

6

Step-by-step explanation:

If 2 of the friends wants to stand beside each other, we can take these 2 friends like 1 option and calculated the number of ways, using the rule of multiplication as:

__ 3_____ * ____2_____ *____1____  =  6

1st place        2nd place        3rd place

Because we have 3 options (2 friends and the friends that are beside each other) for the first place of the picture, 2 options for the second and 1 option for the third.

Answer:

3, 6, and 15

Step-by-step explanation:

Notice that if 60 is a multiple, the numbers in question could have the same factors as 60.

So let's look at 60's prime factors:

60 = 2 * 2 * 3 * 5

we also know that 3 is a factor, so the factor 3 must be included in all three options, we also know that 4 is NOT a factor, so both factors 2 cannot be included (but only one of them could).

So, in order to build the lowest possible numbers that verify such conditions, we can use:

3

3 * 2 = 6

since 3 or 2 cannot be repeated, the next smaller would be:

3 * 5 = 15

Answer:

2+2=4

Step-by-step explanation:

2+2=4

good question like if you have two chocolates and your mom gives you two more than there will be 4 and they will be too delicious

i hope this will help you :)

have a great day

Answer:

2+2=4

Step-by-step explanation:

So you take the 2 numbers 2+2 and you use your finger counting to get to 4. It’s really hard mathematics but you’ll get there. Have a great day!

Answer:2

Step-by-step explanation:

-5.4+8.2=14/5 and then opposite of -2 3/4 is 2.

Answer:

B. (2, 2)

Step-by-step explanation:

In order for the coordinate to be a solution of the systems of inequalities, it has to be in the shaded region (not on the line since both are dotted). Only B fits in the shaded region.

Answer:

second option

Step-by-step explanation:

Given

[tex]x^{4}[/tex] + 6x² + 5 = 0

let u = x², then

u² + 6u + 5 = 0 ← in standard form

(u + 1)(u + 5) = 0 ← in factored form

Equate each factor to zero and solve for u

u + 1 = 0 ⇒ u = - 1

u + 5 = 0 ⇒ u = - 5

Change u back into terms of x, that is

x² = - 1 ( take the square root of both sides )

x = ± [tex]\sqrt{-1}[/tex] = ± i ( noting that [tex]\sqrt{-1}[/tex] = i ), and

x² = - 5 ( take the square root of both sides )

x = ± [tex]\sqrt{-5}[/tex] = ± [tex]\sqrt{5(-1)}[/tex] = ± [tex]\sqrt{5}[/tex] × [tex]\sqrt{-1}[/tex] = ± i[tex]\sqrt{5}[/tex]

Solutions are x = ± i and x = ± i[tex]\sqrt{5}[/tex]

Answer:

bearing of A from C is - 65.24°

the distance |BC| is 187.84 m

Step-by-step explanation:

given data

girl walks AB = 285 m (side c)

bearing angle B = 78°

girl walks AC = 307 m (side a)

solution

we use here the Cosine Law for getting side b that is

ac² = ab² + bc² - 2 × ab × cos(B)     ...............1

307² = 285² + x²  - 2 × 285 cos(78)

x = 187.84 m

and

now we get here angle θ , the bearing from A to C get by law of sines

sin (θ) = [tex]\frac{187.84}{307} \times sin(78)[/tex]

sin (θ) =  0.5985  

θ = 36.76°

and as we get here angle BAC that is

angle BCA = 180 - ( 36.76° + 78° )

angle BCA = 65.24°

and here  negative bearing of A from C so - 65.24°

Answer:

[tex]\displaystyle y = \frac{1}{5}x+1[/tex]

Or:

[tex]x + 5 = 5y[/tex]

Step-by-step explanation:

We have the function:

[tex]y=5x-5[/tex]

And we want to find its inverse.

To find the inverse of a function, we:

Hence:

[tex]x=5y-5[/tex]

Solve for y. Add:

[tex]\displaystyle x + 5 = 5y[/tex]

Divide:

[tex]\displaystyle y = \frac{x+5}{5}[/tex]

Simplify. Hence:

[tex]\displaystyle y = \frac{1}{5}x+1[/tex]

In conclusion, the inverse function is:

[tex]\displaystyle y = \frac{1}{5}x+1[/tex]